Forget about using the 50/1.8 II on any mirrorless system. It has no aperture ring, so there's no aperture control, and you can
only shoot wide open, where the 50/1.8 II is at its absolute softest (sweet spot on that lens is closer to f/4-5.6). And focusing that puppy manually absolutely sucks because of how imprecise and tiny the MF ring at the front of the lens is. If the lens is an FD/FL-mount, not EOS, however, you can use it on any mirrorless.
For autofocus performance the MFT EM-1 is probably your best bet, but at the expense of high ISO noise performance and color rendition that the Fuji X system can do. So you are going to have to compromise depending on what your higher priority is: noise and color or autofocus. You can't have it all, just yet, with mirrorless.
Personally? Given that getting an entire new system is expensive, mirrorless or not, and you want to reuse one of the cheapest lenses Canon makes, if budget is a big issue here, my recommendation would simply be to get a Canon SL1/100D as your go-light body. No new system to get into, that way. And maybe invest in a 40/2.8 STM if you need a tiny lens.
It's sharper than the 50/1.8 II @ f/2.8.